General relativistic solutions with finite self-energy for a point charge under Bopp-Podolsky electromagnetism

TL;DR

This paper presents new solutions in general relativity coupled with Bopp-Podolsky electromagnetism, showing finite self-energy for a point charge and milder singularities than traditional models.

Contribution

It introduces a family of static, spherically symmetric solutions with finite electric-field energy in Einstein-Bopp-Podolsky theory, extending classical Einstein-Maxwell solutions.

Findings

Electric-field energy is finite in these solutions.

Singularity at the charge is milder than Reissner-Nordström.

Solutions feature non-positive bare mass.

Abstract

We establish the existence of a family of static, spherically symmetric spacetimes that are solutions of the Einstein Field Equations of General Relativity coupled to the electric field of a static point charge obeying the equations of electromagnetism of Maxwell-Bopp-Land\'e-Thomas-Podolsky. The point charge is modeled as a naked singularity with non-positive bare mass. The singularity at the location of the charge is milder than that of the Reissner-Weyl-Nordstr\"om solution to the conventional Einstein-Maxwell equations, and, contrary to what happens for the latter, the electric-field energy of these solutions is finite.